We know, that Aaron’s pet tortoise can walk only 1⁄4 km in 1 hour. How far can it walk in half an hour?
Answer
Half an hour covers half of the one-hour distance.
Distance = 1/2 × 1/4 km
= 1/4 divided into 2 equal parts
= 1/8 km
The unit square is cut into 4 rows and 2 columns. One-quarter (top two cells) is halved, and the dark cell is 1 of the 8 equal parts.
Why it happens: cutting the whole into 4 rows and then into 2 columns makes 4 × 2 = 8 equal parts, so each part is 1⁄8 of the whole.
Q2.
Now we divide this 1⁄4 into 2 equal parts. What do we get? What fraction of the whole is shaded?
Answer
The whole is now in 8 equal parts and one of them is shaded.
Whole ÷ 8 equal parts
Shaded = 1 part
= 1/8 of the whole
So 1⁄2 × 1⁄4 = 1⁄8, and the tortoise walks 1⁄8 km in half an hour.
Tip: halving a quarter always gives an eighth — the number of parts doubles, so the size of each part halves.
Q3.
If the tortoise walks faster and it can cover 2⁄5 km in 1 hour, how far will it walk in 3⁄4 of an hour?
Answer
Same two steps: divide by 4, then multiply by 3.
(i) Distance in 1/4 hour = 2/5 ÷ 4
The whole is cut into 5 rows and 4 columns = 20 equal parts
Parts shaded = 2, so distance = 2/20
(ii) Distance in 3/4 hour = 3 × 2/20
= 6/20
= 3/10 km
So 3⁄4 × 2⁄5 = 6⁄20 = 3⁄10.
Why it happens: the 5 rows come from the denominator of the multiplicand and the 4 columns from the denominator of the multiplier. That is exactly why the denominators get multiplied.
Q4.
Using this understanding, multiply 5⁄4 × 3⁄2.
Answer
Draw 3⁄2 as one whole and a half, then cut it into 4 equal parts.
Whole cut into 2 rows and 4 columns = 8 equal parts
3/2 ÷ 4 = 3 of those parts = 3/8
Now multiply by 5:
5/4 × 3/2 = (5 × 3)/8
= 15/8 = 1 7/8
Check it yourself: Brahmagupta's rule gives the same answer straight away — (5 × 3)/(4 × 2) = 15/8. Both numbers are greater than 1, so the product is greater than both. ✔